- #1

Poetria

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- Homework Statement
- Let ##f(x,y)=x^3+y^2+x*y##

Suppose that a point is moving through the plane. At time t , the point is at ## (x(t), y(t))=(t^2, e^{t-1})##. Use linear approximation to estimate the change in f as t goes from 1 to 1.1 . In other words, approximate

- Relevant Equations
- Multivariable chain rule

##f_x=3*x^2+y##

##f_y=2*y+x##

##(3*(t^2)^2+e^{t-1})*2*t+(2*e^{t-1}+t^2)*e^{t-1}##

Well, I am not sure how to evaluate it.

I got a wrong result by multiplying by 0.1, i.e.

##((3*(t^2)^2+e^{t-1})*2*t+(2*e^{t-1}+t^2)*e^{t-1})*0.1##

I guess it is trivial but I am lost. :(

##f_y=2*y+x##

##(3*(t^2)^2+e^{t-1})*2*t+(2*e^{t-1}+t^2)*e^{t-1}##

Well, I am not sure how to evaluate it.

I got a wrong result by multiplying by 0.1, i.e.

##((3*(t^2)^2+e^{t-1})*2*t+(2*e^{t-1}+t^2)*e^{t-1})*0.1##

I guess it is trivial but I am lost. :(